First slide

Theory of equations

Question

If the roots of equation $x^{2} + a^{2} = 8 x + 6 a$ are real, then

Moderate

A

$a \in [2, 8]$
B

$a \in [- 2, 8]$
C

$a \in (2, 8)$
D

$a \in (- 2, 8)$

Solution

Since the roots $x^{2} - 8 x + a^{2} - 6 a = 0$ are real.
$∴ 64 - 4 (a^{2} - 6 a) \geq 0 or a^{2} - 6 a - 16 \leq 0$
$\Rightarrow a \in [- 2, 8]$

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